The Pi You Know Is A Lie(scribd.com)
scribd.com
The Pi You Know Is A Lie
http://www.scribd.com/vacuum?url=http://www.math.utah.edu/~palais/pi.pdf
11 comments
I independently 'discovered' this a few years back, basically on the grounds that there are infinitely many shapes with constant diameter but only one (the circle) with constant radius. It stands to reason that the ratio of a circle's circumference to its diameter contains a spurious factor of 2; it must be that the ratio of circumference to radius is the more fundamental quantity.
This discovery was almost enough to make me want to memorize an embarrassing number of digits of 2π; 6.28 is really pathetic. (What's embarrassing, you say? Try 3.141592653589793238462643383279502884197169399...)
This discovery was almost enough to make me want to memorize an embarrassing number of digits of 2π; 6.28 is really pathetic. (What's embarrassing, you say? Try 3.141592653589793238462643383279502884197169399...)
How are you defining diameter? http://mathworld.wolfram.com/Diameter.html only defines it for circular and spherical objects.
That's what I entered, but it came out on Scribd!
I dislike the current system because it attributes a violation of copyright to the submitter that they're not actually responsible for. In practice it's not a real issue, it's just kind of tacky.
It would be better if all submitted PDFs were turned into Scribd documents, but each user had a profile option for whether to change their PDF links to point to the Scribd doc or to leave it pointing to the original download.
It would be better if all submitted PDFs were turned into Scribd documents, but each user had a profile option for whether to change their PDF links to point to the Scribd doc or to leave it pointing to the original download.
or they might just add a hyperlinked "[pdf]" or "[scribd]" after the original link, pointing to scribdified version.
internets ignoring my choice of pdf viewer -- that sure feels wrong.
oh well, greasemonkey to rescue.
internets ignoring my choice of pdf viewer -- that sure feels wrong.
oh well, greasemonkey to rescue.
Already done: http://userscripts.org/scripts/show/25039
my version (http://userscripts.org/scripts/show/26925) was there 1 minute before that :)
Yeah, I just tacked it on to my blacklist, which I'm sure not everyone wants.
Yeah man. I love this paper. All of the equations look so much prettier without 2 in front of pi everywhere.
Indiana once tried to pass a law saying pi actually equals 3.2
http://www.straightdope.com/classics/a3_341.html
http://www.straightdope.com/classics/a3_341.html
Volume of the n-ball?
Generally, what I would consider the defining equation for pi. Has no factor of 2?
V_n = pi^(n/2)R^n / Gamma(n/2+1) = C_n R^n
C_n = pi^k/k! for even n=2k
C_n = 2^(k+1)k!pi^k / (2k+1)! for odd n=2k+1
Of course we could just change the definition of gamma, but I prefer gamma as an extension of factorial.
Generally, what I would consider the defining equation for pi. Has no factor of 2?
V_n = pi^(n/2)R^n / Gamma(n/2+1) = C_n R^n
C_n = pi^k/k! for even n=2k
C_n = 2^(k+1)k!pi^k / (2k+1)! for odd n=2k+1
Of course we could just change the definition of gamma, but I prefer gamma as an extension of factorial.
Almost as bad as negatively charged electrons.
I don't see why this is such a big deal. Scaling by a factor of 2 doesn't make any of the math lose it's beauty. The underlying math is still the same. Calling 30 minutes "an hour" doesn't make time go faster. It's all semantics, really.
Anyway, pi is so engrained in our mathematics that the costs of switching would surely be higher than any superficial, aesthetic benefits.
Anyway, pi is so engrained in our mathematics that the costs of switching would surely be higher than any superficial, aesthetic benefits.
The author knows this, and was making a merely aesthetic point which you seem to have sucked all the fun out of.
I think the aesthetics are important. You can see further when they are better.
The three legged symbol is pretty good, but maybe papers could just set the value of pi at the introduction.
Holy... Eliezer Yudkowsky? Why, hello...!
Wowsers, that's a good point. I didn't know he's on YC, that's great.
Aw, shucks.
From the article: The proper value, which does deserve all of the reverence and adulation bestowed upon the current imposter, is the number now unfortunately known as 2pi.
Does this mean we can have 2pi day on Jun 28?
Does this mean we can have 2pi day on Jun 28?
edit: Try zooming all the way in. You're in for some hideously unreadable fuzzy font rendering... why oh why.